Estimating and interpreting the instantaneous frequency of a signal. II. Algorithms and applications
01 Apr 1992-Vol. 80, Iss: 4, pp 540-568
TL;DR: The concept of instantaneous frequency (IF) is extended to discrete-time signals and methods based on a modeling of the signal phase as a polynomial have been introduced.
Abstract: For pt.I see ibid., vol.80, no.4, p.520-38 (1992). The concept of instantaneous frequency (IF) is extended to discrete-time signals. The specific problem explored is that of estimating the IF of frequency-modulated (FM) discrete-time signals embedded in Gaussian noise. Well-established methods for estimating the IF include differentiation of the phase and smoothing thereof, adaptive frequency estimation techniques such as the phase locked loop (PLL), and extraction of the peak from time-varying spectral representations. More recently, methods based on a modeling of the signal phase as a polynomial have been introduced. These methods are reviewed, and their performance compared on both simulated and real data. Guidelines are given as to which estimation method should be used for a given signal class and signal-to-noise ratio (SNR). >
Citations
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TL;DR: A set of simple new procedures has been developed to enable the real-time manipulation of speech parameters by using pitch-adaptive spectral analysis combined with a surface reconstruction method in the time–frequency region.
1,741 citations
Cites background from "Estimating and interpreting the ins..."
...However, there is no reason for the 1 0 extracted in that manner to agree with the instantaneous frequency[5, 6, 1, 2] of the fundamental component in Equation 1....
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TL;DR: Time-frequency domain signal processing using energy concentration as a feature is a very powerful tool and has been utilized in numerous applications and the expectation is that further research and applications of these algorithms will flourish in the near future.
646 citations
Cites background from "Estimating and interpreting the ins..."
...Interested readers should refer to [263,264] for details....
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TL;DR: This paper offers an overview of the difficulties involved in using AS, and two new methods to overcome the difficulties for computing IF, and finds that the NHT and direct quadrature gave the best overall performance.
Abstract: Instantaneous frequency (IF) is necessary for understanding the detailed mechanisms for nonlinear and nonstationary processes. Historically, IF was computed from analytic signal (AS) through the Hilbert transform. This paper offers an overview of the difficulties involved in using AS, and two new methods to overcome the difficulties for computing IF. The first approach is to compute the quadrature (defined here as a simple 90° shift of phase angle) directly. The second approach is designated as the normalized Hilbert transform (NHT), which consists of applying the Hilbert transform to the empirically determined FM signals. Additionally, we have also introduced alternative methods to compute local frequency, the generalized zero-crossing (GZC), and the teager energy operator (TEO) methods. Through careful comparisons, we found that the NHT and direct quadrature gave the best overall performance. While the TEO method is the most localized, it is limited to data from linear processes, the GZC method is the m...
618 citations
TL;DR: The authors define the discrete polynomial-phase transform, derive its basic properties, and use it to develop computationally efficient estimation and detection algorithms.
Abstract: The discrete polynomial-phase transform (DPT) is a new tool for analyzing constant-amplitude polynomial-phase signals. The main properties of the DPT are its ability to identify the degree of the phase polynomial and to estimate its coefficients. The transform is robust to deviations from the ideal signal model, such as slowly-varying amplitude, additive noise and nonpolynomial phase. The authors define the DPT, derive its basic properties, and use it to develop computationally efficient estimation and detection algorithms. A statistical accuracy analysis of the estimated parameters is also presented. >
381 citations
TL;DR: This paper proposes and analyzes two new frequency estimators that interpolate on the Fourier coefficients of the received signal samples that achieve identical asymptotic performances.
Abstract: The estimation of the frequency of a complex exponential is a problem that is relevant to a large number of fields. In this paper, we propose and analyze two new frequency estimators that interpolate on the Fourier coefficients of the received signal samples. The estimators are shown to achieve identical asymptotic performances. They are asymptotically unbiased and normally distributed with a variance that is only 1.0147 times the asymptotic Crame/spl acute/r-Rao bound (ACRB) uniformly over the frequency estimation range.
370 citations
References
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Book•
01 Jan 1986
TL;DR: In this paper, the authors propose a recursive least square adaptive filter (RLF) based on the Kalman filter, which is used as the unifying base for RLS Filters.
Abstract: Background and Overview. 1. Stochastic Processes and Models. 2. Wiener Filters. 3. Linear Prediction. 4. Method of Steepest Descent. 5. Least-Mean-Square Adaptive Filters. 6. Normalized Least-Mean-Square Adaptive Filters. 7. Transform-Domain and Sub-Band Adaptive Filters. 8. Method of Least Squares. 9. Recursive Least-Square Adaptive Filters. 10. Kalman Filters as the Unifying Bases for RLS Filters. 11. Square-Root Adaptive Filters. 12. Order-Recursive Adaptive Filters. 13. Finite-Precision Effects. 14. Tracking of Time-Varying Systems. 15. Adaptive Filters Using Infinite-Duration Impulse Response Structures. 16. Blind Deconvolution. 17. Back-Propagation Learning. Epilogue. Appendix A. Complex Variables. Appendix B. Differentiation with Respect to a Vector. Appendix C. Method of Lagrange Multipliers. Appendix D. Estimation Theory. Appendix E. Eigenanalysis. Appendix F. Rotations and Reflections. Appendix G. Complex Wishart Distribution. Glossary. Abbreviations. Principal Symbols. Bibliography. Index.
16,062 citations
Book•
01 Jan 1985TL;DR: This chapter discusses Adaptive Arrays and Adaptive Beamforming, as well as other Adaptive Algorithms and Structures, and discusses the Z-Transform in Adaptive Signal Processing.
Abstract: GENERAL INTRODUCTION. Adaptive Systems. The Adaptive Linear Combiner. THEORY OF ADAPTATION WITH STATIONARY SIGNALS. Properties of the Quadratic Performance Surface. Searching the Performance Surface. Gradient Estimation and Its Effects on Adaptation. ADAPTIVE ALGORITHMS AND STRUCTURES. The LMS Algorithm. The Z-Transform in Adaptive Signal Processing. Other Adaptive Algorithms and Structures. Adaptive Lattice Filters. APPLICATIONS. Adaptive Modeling and System Identification. Inverse Adaptive Modeling, Deconvolution, and Equalization. Adaptive Control Systems. Adaptive Interference Cancelling. Introduction to Adaptive Arrays and Adaptive Beamforming. Analysis of Adaptive Beamformers.
5,645 citations
01 Jul 1989
TL;DR: A review and tutorial of the fundamental ideas and methods of joint time-frequency distributions is presented with emphasis on the diversity of concepts and motivations that have gone into the formation of the field.
Abstract: A review and tutorial of the fundamental ideas and methods of joint time-frequency distributions is presented. The objective of the field is to describe how the spectral content of a signal changes in time and to develop the physical and mathematical ideas needed to understand what a time-varying spectrum is. The basic gal is to devise a distribution that represents the energy or intensity of a signal simultaneously in time and frequency. Although the basic notions have been developing steadily over the last 40 years, there have recently been significant advances. This review is intended to be understandable to the nonspecialist with emphasis on the diversity of concepts and motivations that have gone into the formation of the field. >
3,568 citations
Book•
01 Jan 1975TL;DR: Feyman and Wing as discussed by the authors introduced the simplicity of the invariant imbedding method to tackle various problems of interest to engineers, physicists, applied mathematicians, and numerical analysts.
Abstract: sprightly style and is interesting from cover to cover. The comments, critiques, and summaries that accompany the chapters are very helpful in crystalizing the ideas and answering questions that may arise, particularly to the self-learner. The transparency in the presentation of the material in the book equips the reader to proceed quickly to a wealth of problems included at the end of each chapter. These problems ranging from elementary to research-level are very valuable in that a solid working knowledge of the invariant imbedding techniques is acquired as well as good insight in attacking problems in various applied areas. Furthermore, a useful selection of references is given at the end of each chapter. This book may not appeal to those mathematicians who are interested primarily in the sophistication of mathematical theory, because the authors have deliberately avoided all pseudo-sophistication in attaining transparency of exposition. Precisely for the same reason the majority of the intended readers who are applications-oriented and are eager to use the techniques quickly in their own fields will welcome and appreciate the efforts put into writing this book. From a purely mathematical point of view, some of the invariant imbedding results may be considered to be generalizations of the classical theory of first-order partial differential equations, and a part of the analysis of invariant imbedding is still at a somewhat heuristic stage despite successes in many computational applications. However, those who are concerned with mathematical rigor will find opportunities to explore the foundations of the invariant imbedding method. In conclusion, let me quote the following: "What is the best method to obtain the solution to a problem'? The answer is, any way that works." (Richard P. Feyman, Engineering and Science, March 1965, Vol. XXVIII, no. 6, p. 9.) In this well-written book, Bellman and Wing have indeed accomplished the task of introducing the simplicity of the invariant imbedding method to tackle various problems of interest to engineers, physicists, applied mathematicians, and numerical analysts.
3,249 citations